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finitely many triples of positive (a, b, c) such that 1/a + 1/b + 1/c = 1/1000

Source: 1967 Swedish Mathematical Competition p3

March 21, 2021

Diophantine equationdiophantinenumber theory

Problem Statement

Show that there are only finitely many triples

(a, b, c)

of positive integers such that

\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{1}{1000}